I have created a number of custom menu slots in my WordPress theme, and the output of the links into them has been very easy. Unfortunately I cannot find a way to output the user entered title for the menu above the list in each menu slot. This doesn't seem to come with the default WordPress function.

I am wondering if there is a simple and efficient way to grab the user entered name of the menu that is currently in a slot in my theme. [Somewhat like the way the widgets function allows you to chose whether you want to show the title of the specific widget.]

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Read the source code to see how that text is being stored and if there's a getter for it. If not, read it from the database yourself.
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Dan GrossmanJul 5 '11 at 3:10

The issue with that is that I don't know of a way to get the ID of the current custom menu in a specific menu slot. Since they have the ability to add the menu's in any order they desire.
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BorisKourtJul 16 '11 at 21:37